1. Technical Field of the Invention
The present invention relates to a method for storing substantial data which can unify CAD and simulation by storing the substantial data that integrates a shape and physical properties by a small storage capacity, and more particularly to a method and a program for converting boundary data into cell inner shape data.
2. Description of the Related Art
In a field of advanced research and development/technical developments, a higher level/complexity thereof has made a great many trials and errors absolutely necessary, increasing risks in the middle of developments. In Japan that depends on science and technology for its survival, it is extremely important to achieve an unprecedentedly high level/efficiency of a development process by eliminating such risks as many as possible.
In the field of research and development/technical developments, computer aided design (CAD), computer aided manufacturing (CAM), computer aided engineering (CAE), computer aided testing (CAT), and the like are currently used as simulation means of designing, fabricating, analyzing and testing.
Because of the present invention, it is expected that cooperative simulation (C-Simulation) which is continuous simulation, advanced CAM (A-CAM) which takes a fabrication process into consideration, deterministic fabrication (D-fabrication) which can achieve ultimate accuracy, and the like will come into wide use.
According to such conventional simulation means, data of an object is stored based on constructive solid geometry (CSG) or boundary representation (B-rep).
In the case of the CSG, however, the entire object is stored as an aggregation of very small solid models. Consequently, if data is heavy and simulation means (software or the like) is mounted, enormous data must be processed, causing a problem of much time necessary for analysis even when a large scale computer is used.
In the case of the B-rep, the object is represented by a boundary. Thus, while data is light and an amount of data is small, there is not direct information regarding the inside of a boundary surface, causing a problem of unsuitability to deformation analysis or the like if no change is made.
Furthermore, according to the conventional data storage means, each time thermal/fluid analysis, large solid analysis, coupled analysis thereof or the like is carried out, division is made in a mesh form or the like suited to the analysis, and a result of the analysis can be displayed or the like to apply a finite element method or the like. However, unification of CAD and simulation is difficult, causing a problem of impossibility of managing the processes of designing, analyzing, fabricating, assembling, testing and the like based on the same data.
In other words, the following problems are inherent in the current solid/surface-CAD (referred to as S-CAD hereinafter):    (1) data is not passed, inferior in internal conversion operation (problems of numerical value error and processing method);    (2) direct use is impossible for simulation (mesh must be formed); and    (3) investigation of fabrication by CAM is impossible (only last shape is given).
Additionally, the following problems are inherent in fabrication:    (1) a fabrication process cannot be represented (rough fabrication or process design assistance is insufficient);    (2) dealing with a new fabrication method such as laser fabrication or superadvanced fabrication is impossible (only cutting is available, numerical value accuracy is insufficient); and    (3) a fabrication method itself cannot be selected (different material characteristics are given in compound material).
To solve the aforementioned problems, the inventors et. al have invented “METHOD FOR STORING SUBSTANTIAL DATA THAT INTEGRATES SHAPE AND PHYSICAL PROPERTIES”, and applied for a patent (Japanese Patent Application No. 2001-25023, not laid-open).
According to this invention, as schematically shown in FIG. 1, external data constituted of boundary data of an object is divided into cubic cells by oct-tree division in which boundary surfaces cross each other, and the cells are classified into a nonboundary cell 13a which includes no boundary surface and a boundary cell 13b which includes a boundary surface. In the drawing, a reference numeral 15 is a cutting point.
According to this invention, various physical property values are stored for each cell, and substantial data that integrates shapes and physical properties can be stored by a small storage capacity. Thus, a shape, a structure, physical property information, and hysteresis are managed in a unified manner to enable management of data regarding a series of processes from designing to fabricating, assembling, testing, evaluation and the like based on the same data, whereby it is possible to unify CAD and simulation.
The aforementioned method for storing the substantial data is referred to as “volume CAD” or “V-CAD” hereinafter. In the present application, the V-CAD is defined as follows: “V-CAD means that a boundary surface is formed in a cell of a voxel dataset”.
According to conventional CAD, even a solid is in fact hollow papier-mache stage data as in the case of the B-rep or the like. On the other hand, according to the V-CAD, even the inside is stuffed, and physical data can be held. Because of internal information that has been provided, it is expected that geometrical calculation which tends to break down in shape processing of the B-rep or the like can be strongly carried out. Further, the V-CAD goes beyond a framework of a simple tool to represent shapes, and is designed to provide a data foundation which can be directly used for simulation and fabrication. In order to truly achieve a system of such “manufacturing”, a simulation technology or a fabrication technology must be simultaneously developed to effectively use the V-CAD. Especially, for fabrication, only data of a surface shape has been used. Therefore, it can be said that there are almost no fabrication technologies capable of truly utilizing volume data except laser stereolithography and rapid prototyping (3D ink jet).
From the viewpoint of the current situation of a manufacturing world, it is very important to generate volume data in the V-CAD by reading a shape represented by the conventional type CAD. Thus, according to the V-CAD, it is necessary to possess boundary data which enables reconstruction of a boundary of shape data (external data) in a boundary cell.
Conventionally, it is marching cubes (abbreviated to MC hereinafter) that have generally been used for generating a polygon from volume data. For example, the MC is introduced in the following Document 1:
(Document 1) “MARCHING CUBES: A HIGH RESOLUTION 3D SURFACE CONSTRUCTION ALGORITHM”, Computer Graphics, Volume 21, Number 4, July 1987.
For reference, FIGS. 2a to 2d show all cutting point patterns and boundary segments of two-dimensional MC, and FIGS. 3a to 3n show all cutting point patterns (boundary surfaces are omitted) of three-dimensional MC.
In the case of the three-dimensional MC, positive and negative numerical values are written in 8 vertexes of a three-dimensional cell (cube), and isosurfaces are generated based on these numerical values (isosurfaces of zero values are considered hereinafter). One cutting point is disposed on an edge if signs (positive or negative) of numerical values of both ends of the edge of the cube do not match each other. No cutting point is disposed if they match each other. This operation is carried out for 12 edges of the cube, and then planes are formed based on cutting points. The same holds true for the two-dimensional MC.
FIGS. 4a to 4c are exemplary views showing a difference of cutting points in rectangular cells between MC and Kitta cubes (KTC). In the examples, in the case of the MC, 4 vertexes (white circles) of a square cell have the same sign as they are located outside a shape (closed curve) in a situation as shown in FIG. 4a, and thus no cutting points are generated on 4 edges (4 sides) of the cell. As a result, no approximate isosurfaces are formed at all in this case. This means that current resolution is too rough to represent the shape from the standpoint of the MC. Therefore, in the MC of the example, there is a problem of impossibility of representing the cutting points of the 4 edges of the cell as in the case of FIG. 4b or 4c. FIG. 4a shows an extreme example. Essentially similar defects frequently occur, and FIG. 4d shows an defect example. Such defects frequently occur at an intersection of a curved boundary surface and a cell edge. In the case of the KTC, this situation is approximated as shown in FIG. 4f. In the case of the MC, it is approximated as shown in FIG. 4g. FIGS. 4c and 4f show two-dimensional examples. In three-dimensional representation, more cases can be represented only by the KTC. It can be understood that the KTC has much richer power of representation than the MC at equal resolution.
On the other hand, according to the present invention (KTC) described later, two cutting points are generated on each of 4 edges as shown in FIG. 4b. If the number of cutting points is limited to 0 or 1 on one edge, representation as shown in FIG. 4c can be obtained.
FIGS. 5a and 5b are views showing a difference of cutting points on edges between the conventional MC and the KTC of the present invention. When the MC is constructed, the number of cutting points is limited to 0 or 1 on one edge. As illustrated in FIG. 5a, in the case of the MC, one cutting point is generated on an edge only when signs of both ends of each edge of a cell oppose each other (positive and negative values). Thus, as shown in FIG. 5b, when a cutting point is given on one edge, signs of both edges may not only oppose each other (positive and negative values) but also match each other. In the case of the MC, a cutting point can be represented only in a part of such cases.
In FIGS. 4a to 4c, in the case of the MC, the cell must be subdivided to represent a shape indicated by a closed solid line. As a result, in the V-CAD that uses the MC, subdivision of the cell becomes necessary to hold boundary data, and a storage capacity to store substantial data that integrates the shape and physical properties is accordingly increased exponentially. Furthermore, prevention of an increase in the storage capacity causes a difficulty of precisely representing a shape of a boundary part.